Viscosity dynamic uniaxial extensional

Table I. Dynamic Uniaxial Extensional Viscosities and Shear Viscosities...

Figure 6. Dynamic uniaxial extensional viscosities of coal-water fuels formulated with different stabilizers.

DYNAMIC UNIAXIAL EXTENSIONAL VISCOSITIES AND THEIR IMPORTANCE IN THE MECHANICAL STABILITY OF WATER-SOLUBLE CARBOHYDRATE POLYMER SOLUTIONS... 

In mechanical degradation, chain scission does not occur from individual attack on a specific atom of the macromolecular chain, but from the application of a critical stress. The extensional viscosities of high-molecular-weight, synthetic polymers have been studied for the past two decades, in attempts to relate the values with drag reduction behavior. To date the dynamic uniaxial extensional viscosities of aqueous carbohydrate solutions have not been reported. 

S. Soyles, D.A. Dinga, G.P. Glass, J.E. Dynamic Uniaxial Extensional Viscosity. Response in Spray Applications, Polymers as Rheology Modifiers, ACS 462 (1991)... 

Figure 3.19 The polymer contribution to the steady-state uniaxial extensional viscosity r divided by the polymer contribution to the zero-shear viscosity rjp = r/o — fjj for the dumbbell model with a nonlinear FENE spring and various values of B = ipL. (From Bird et al. Dynamics of Polymeric Liquids, Vol. 2, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

Three HIPS resins possessing distinct rheological properties were utilized in this study STYRON 1200, 1170, and 484. These resins have melt flow rates (MFR) of 5.0, 2.1, and 2.8 g/10 min (200T05kg) and will be referred to in the paper as HIPS 1, HIPS 2, and HIPS 3, respectively. The dynamic mechanical spectroscopy measurements (viscosity vs. frequency and temperature, loss and storage modulus vs. frequency and temperature) were performed on a TA Instruments ARES rheometer. The measurements were obtained at three different temperatures 170, 190, 210, and 2301C. The uniaxial extensional viscosity measurements were performed at three Hencky rates 0.1, and 10s on a SER (Sentmanat Extensional Rheometer, Xpansion Instruments) at 1701C. 

Material functions must however be considered with respect to the mode of deformation and whether the applied strain is constant or not in time. Two simple modes of deformation can be considered simple shear and uniaxial extension. When the applied strain (or strain rate) is constant, then one considers steady material functions, e.g. q(y,T) or ri (e,T), respectively the shear and extensional viscosity functions. When the strain (purposely) varies with time, the only material functions that can realistically be considered from an experimental point of view are the so-called dynamic functions, e.g. G ((D,y,T) and ri (a), y,T) or E (o),y,T) and qg(o),y, T) where the complex modulus G (and its associated complex viscosity T] ) specifically refers to shear deformation, whilst E and stand for tensile deformation. It is worth noting here that shear and tensile dynamic deformations can be applied to solid systems with currently available instruments, whUst in the case of molten or fluid systems, only shear dynamic deformation can practically be experimented. There are indeed experimental and instrumental contingencies that severely limit the study of polymer materials in the conditions of nonlinear viscoelasticity, relevant to processing. 

Rheological measurements are performed so as to obtain a test fluid s material functions. Under viscometric flows we have seen that the shear viscosity and the primary and secondary normal stress differences suffice to rheologically characterize the fluid. If the flow field is extensional and the material is able to attain a state of dynamic equilibrium, then one measures the extensional viscosity otherwise, we measure the extensional viscosity growth or decay functions. In this section, we will examine steady and dynamic shear plus uniaxial extensional tests, since these make up the majority of routine rheological characterization. 

Here k, t]o, and f are found from steady shear and dynamic data. The parameter s is obtained from extensional viscosity data and has little effect on the prediction of the shear flow properties. Actually, tjq can be replaced by riiy) or a set of values for , and A,. Predictions of the model for steady shear and uniaxial extensional flows are summarized in Table 3.1. The choice of the exponential function allows one to predict values of ij which increase with s and then pass through a maximum. 

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